Inconsistant behavior when re-linking missing textures. sRGB and Non-Color mismatches
When opening a new texture, Blender doesn't know it's meant to be a single user copy.
You should Remap the old texture instead, so it'll change for all materials at once.

Add your 'new texture.jpg', with a second copy (new texture.001) for the non-color variant
Open Outliner &gt; Scene
Right click the 'old texture.jpg' and go &gt; Remap users &gt; 'new texture.jpg' &gt; OK.